Vertical Line Test

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.

Front

What does it mean for a graph to be a function?

Back

A graph is a function if every input (x-value) has exactly one output (y-value).

Front

How can you determine if a graph is not a function?

Back

A graph is not a function if a vertical line can be drawn that intersects the graph at more than one point.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; this would violate the definition of a function.

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What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is the set of points that form a circle, as a vertical line can intersect the circle at two points.

Front

What is the significance of the Vertical Line Test in mathematics?

Back

The significance of the Vertical Line Test is that it provides a visual way to determine if a graph represents a function, which is fundamental in understanding relations.

Front

What is the difference between a function and a non-function?

Back

A function has a unique output for each input, while a non-function may have multiple outputs for a single input.

Front

How can you visually identify a function from its graph?

Back

You can visually identify a function from its graph by using the Vertical Line Test; if any vertical line crosses the graph more than once, it is not a function.